= Pseudohyperbolic distance
{title2=$\delta(z,w)=|(z-w)/(1-\overline wz)|$}
On the <unit disc>, the <pseudohyperbolic distance> is
$$
\delta(z,w)=\left|\frac{z-w}{1-\overline wz}\right|.
$$
It is invariant under disc <Möbius transformations>. For the curvature-minus-one <hyperbolic metric> with length element $2|dz|/(1-|z|^2)$, $\delta(z,w)=\tanh(\rho(z,w)/2)$ and $e^{-\rho(z,w)}=(1-\delta)/(1+\delta)$. The <Schwarz-Pick theorem> says that <holomorphic functions> from the disc into itself contract this distance. A <Blaschke factor> has modulus $\delta(z,a)$, so the distance also controls the size of a product with prescribed zeros.
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